Invariants of linear parabolic differential equations

The paper is dedicated to construction of invariants for the parabolic equation u t + a ( t , x ) u xx + b ( t , x ) u x + c ( t , x ) u = 0 . We consider the equivalence group given by point transformations and find all invariants up to seventh-order, i.e. the invariants involving the derivatives up to seventh-order of the coefficients a, b and c with respect to the independent variables t, x.